LOS ANGELES—Toyota Motor Corp., moving to put years of legal problems behind it, has agreed to pay more than $1 billion to settle dozens of U.S. lawsuits relating to sudden acceleration.

The proposed deal, filed Wednesday in federal court, would be among the largest ever paid out by an automaker.

It applies to numerous suits claiming economic damages caused by safety defects in the automaker’s vehicles, but does not cover dozens of personal injury and wrongful-death suits that are still pending around the United States.

The suits were filed over the last three years by Toyota and Lexus owners who claimed that the value of their vehicles had been hurt by the potential for defects, including floor mats that could cause the vehicles to surge out of control.

In addition, Toyota said it is close to settling suits filed by the Orange County district attorney and a coalition of state attorneys general who had accused the automaker of deceptive business practices. The costs of those agreements would be included in a $1.1-billion charge the Japanese automaker said it will take against earnings to cover the actions.

“We concluded that turning the page on this legacy legal issue through the positive steps we are taking is in the best interests of the company, our employees, our dealers and, most of all, our customers,” Christopher Reynolds, Toyota’s chief counsel in the U.S., said in a statement.

Toyota’s lengthy history of sudden acceleration was the subject of a series of Los Angeles Times articles in 2009 after a horrific crash outside San Diego took the life of an off-duty California Highway Patrol officer and his family.

Under terms of the agreement, which has not yet been approved in court, Toyota would install brake override systems in numerous models and provide cash payments from a $250-million fund to owners whose vehicles cannot be modified to incorporate that safety measure.

In addition, the automaker plans to offer extended repair coverage on throttle systems in 16 million vehicles and offer cash payments from a separate $250-million fund to Toyota and Lexus owners who sold their vehicles or turned them in at the end of a lease in 2009 or 2010.

The total value of the settlement could reach $1.4 billion, according to Steve Berman, the lead plaintiff attorney in the case.

The lawsuits, filed over the last several years, had been seeking class certification.

News of the agreement comes scarcely a week after Toyota agreed to pay a record $17.35 million fine to the National Highway Traffic Safety Administration for failing to report a potential floor mat defect in a Lexus SUV. Those come on top of almost $50 million in fines paid by Toyota for other violations related to sudden acceleration since 2010.

The massive settlement does not, however, put Toyota’s legal woes to rest. The automaker still faces numerous injury and wrongful death claims around the country, including a group of cases that have been consolidated in federal court in Santa Ana, Calif., and other cases awaiting trial in Los Angeles County.

Toyota spokesman Mike Michels said Wedneday’s proposed settlement would have no bearing on the personal injury cases.

“All carmakers face these kinds of suits,” he said. “We’ll defend those as we normally would.”

The giant automaker’s sudden-acceleration problems first gained widespread attention after the August 2009 crash of a Lexus ES outside San Diego.

That accident set off a string of recalls, an unprecedented decision to temporarily stop sales of all Toyota vehicles and a string of investigations, including a highly unusual apology by Toyota president Akio Toyoda before a congressional committee. Eventually Toyota recalled more than 10 million vehicles worldwide and has since spent huge sums — estimated at more than $2 billion, not including Wednesday’s proposed settlement — to repair both its automobiles and public image.

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